[petsc-users] What does PCASMSetOverlap do?

[Zhuo Chen]

Dear Pierre,

Thank you! I looked into the webpage you sent me and I think it is not the
situation that I am talking about.

I think I need to attach a figure for an illustrative purpose. This figure
is Figure 14.5 of "Iterative Method for Sparse Linear Systems" by Saad.
[image: domaindecompostion.png]

If I divide the domain into these three subdomains, as you can see, the
middle block has two interfaces. In the matrix form, its rows are not
contiguous, i.e., distributed in different processors. If ASM only expands
in the contiguous direction, the domain decomposition become ineffective, I
guess.



On Wed, Apr 13, 2022 at 9:36 PM Pierre Jolivet <pierre at joliv.et> wrote:

>
>
> On 13 Apr 2022, at 3:30 PM, Zhuo Chen <chenzhuotj at gmail.com> wrote:
>
> Dear Matthew and Mark,
>
> Thank you very much for the reply! Much appreciated!
>
> The question was about a 1D problem. I think I should say core 1 has row
> 1:32 instead of 1:32, 1:32 as it might be confusing.
>
> So the overlap is extended to both directions for the middle processor but
> only toward the increasing direction for the first processor and the
> decreasing direction for the last processor. In 1D, this makes sense as the
> domain is contiguous. However, in 2D with domain decomposition with spacial
> overlaps, this overlapping would not work as one subdomain can have several
> neighbor domains. Mark mentioned generalized ASM, is that the correct
> direction that I should look for?
>
>
> What is it that you want to do exactly?
> If you are using a standard discretisation kernel, e.g., piecewise linear
> finite elements, MatIncreaseOverlap() called by PCASM will generate an
> overlap algebraically which is equivalent to the overlap you would have
> gotten geometrically.
> If you know that “geometric” overlap (or want to use a custom definition
> of overlap), you could use
> https://petsc.org/release/docs/manualpages/PC/PCASMSetLocalSubdomains.html
>
> Thanks,
> Pierre
>
> Best regards.
>
>
> On Wed, Apr 13, 2022 at 9:14 PM Matthew Knepley <knepley at gmail.com> wrote:
>
>> On Wed, Apr 13, 2022 at 9:11 AM Mark Adams <mfadams at lbl.gov> wrote:
>>
>>>
>>>
>>> On Wed, Apr 13, 2022 at 8:56 AM Matthew Knepley <knepley at gmail.com>
>>> wrote:
>>>
>>>> On Wed, Apr 13, 2022 at 6:42 AM Mark Adams <mfadams at lbl.gov> wrote:
>>>>
>>>>> No, without overlap you have, let say:
>>>>> core 1:   1:32, 1:32
>>>>> core 2:   33:64,  33:64
>>>>>
>>>>> Overlap will increase the size of each domain so you get:
>>>>> core 1:   1:33, 1:33
>>>>> core 2:   32:65,  32:65
>>>>>
>>>>
>>>> I do not think this is correct. Here is the algorithm. Imagine the
>>>> matrix is a large graph. When you divide rows, you
>>>> can think of that as dividing the vertices into sets. If overlap = 1,
>>>> it means start with my vertex set, and add all vertices
>>>> that are just 1 edge away from my set.
>>>>
>>>
>>> I think that is what was said. You increase each subdomain by one row of
>>> vertices.
>>> So in 1D, vertex 32 and 33 are in both subdomains and you have an
>>> overlap region of size 2.
>>> They want an overlap region of size 1, vertex 33.
>>>
>>
>> This is true, but I did not think they specified a 1D mesh.
>>
>>   Matt
>>
>>
>>>
>>>>   Thanks,
>>>>
>>>>      Matt
>>>>
>>>>
>>>>> What you want is reasonable but requires PETSc to pick a separator
>>>>> set, which is not well defined.
>>>>> You need to build that yourself with gasm (I think) if you want this.
>>>>>
>>>>> Mark
>>>>>
>>>>> On Wed, Apr 13, 2022 at 3:17 AM Zhuo Chen <chenzhuotj at gmail.com>
>>>>> wrote:
>>>>>
>>>>>> Hi,
>>>>>>
>>>>>> I hope that everything is going well with everybody.
>>>>>>
>>>>>> I have a question about the PCASMSetOverlap. If I have a 128x128
>>>>>> matrix and I use 4 cores with overlap=1. Does it mean that from core 1 to
>>>>>> core 4, the block ranges are (starting from 1):
>>>>>>
>>>>>> core 1:   1:33, 1:33
>>>>>> core 2:   33:65,  33:65
>>>>>> core 3:   65:97,  65:97
>>>>>> core 4:   95:128, 95:128
>>>>>>
>>>>>> Or is it something else? I cannot tell from the manual.
>>>>>>
>>>>>> Many thanks in advance.
>>>>>>
>>>>>>
>>>>>>
>>>>>> --
>>>>>> Zhuo Chen
>>>>>> Department of Astronomy
>>>>>> Tsinghua University
>>>>>> Beijing, China 100084
>>>>>> *https://czlovemath123.github.io/ <https://czlovemath123.github.io/>*
>>>>>>
>>>>>
>>>>
>>>> --
>>>> What most experimenters take for granted before they begin their
>>>> experiments is infinitely more interesting than any results to which their
>>>> experiments lead.
>>>> -- Norbert Wiener
>>>>
>>>> https://www.cse.buffalo.edu/~knepley/
>>>> <http://www.cse.buffalo.edu/~knepley/>
>>>>
>>>
>>
>> --
>> What most experimenters take for granted before they begin their
>> experiments is infinitely more interesting than any results to which their
>> experiments lead.
>> -- Norbert Wiener
>>
>> https://www.cse.buffalo.edu/~knepley/
>> <http://www.cse.buffalo.edu/~knepley/>
>>
>
>
> --
> Zhuo Chen
> Department of Astronomy
> Tsinghua University
> Beijing, China 100084
> *https://czlovemath123.github.io/ <https://czlovemath123.github.io/>*
>
>
>

-- 
Zhuo Chen
Department of Astronomy
Tsinghua University
Beijing, China 100084
*https://czlovemath123.github.io/ <https://czlovemath123.github.io/>*
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